Related papers: Nonlocal coupling among oscillators mediated by a …
Synchronization commonly occurs in many natural and man-made systems, from neurons in the brain to cardiac cells to power grids to Josephson junction arrays. Transitions to or out of synchrony for coupled oscillators depend on several…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
The synchronization of oscillator ensembles is pervasive throughout nonlinear science, from classical or quantum mechanics to biology, to human assemblies. Traditionally, the main focus has been the identification of threshold parameter…
A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability…
We consider a model for two lasers that are mutually coupled optoelectronically by modulating the pump of one laser with the intensity deviations of the other. Signal propagation time in the optoelectronic loop causes a significant delay…
The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks…
We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications.…
We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is…
We study a model of a nonlinear oscillator with a random frequency and derive the asymptotic behavior of the probability distribution function when the noise is white. In the small damping limit, we show that the physical observables grow…
Arrays of identical limit-cycle oscillators have been used to model a wide variety of pattern-forming systems, such as neural networks, convecting fluids, laser arrays, and coupled biochemical oscillators. These systems are known to exhibit…
In this letter, we report a numerical study on the collective dynamics of two mutually coupled Thomas oscillators with linear/nonlinear coupling in a dynamic environment. We claim our model calculations can explain the diffusion of…
We introduce a novel coupling scheme for maximizing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency…
We study classical binary fluid mixtures in which densities vary on very short time (ps) and length (nm) scales, such that hydrodynamics does not apply. In a pure fluid with a localized heat pulse the breakdown of hydrodynamics was overcome…
We consider the Kuramoto model of an ensemble of interacting oscillators allowing for an arbitrary distribution of frequencies and coupling strengths. We define a family of traveling wave states as stationary in a rotating frame, and derive…
In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time and ensemble average mean squared displacement are remarkably different. The ensemble average diffusivity is…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the…
Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…
Large ensembles of heterogeneous oscillators often exhibit collective synchronization as a result of mutual interactions. If the oscillators have distributed natural frequencies and common shear (or nonisochronicity), the transition from…